Decorations for school dances take 1/5 of the student council's budget. entertainment takes 3/10 of the budget. what fraction of the budget is left? include !

We need to find out the total amount of budget used and then subtract from 1.

first, we need to find 1/5 + 3/10. in order to add these, we need to find a common denominator. because 5 divides 10 evenly, it would be easiest to use 10 as a denominator.

3/10 already has 10 in the denominator, so we don't have to touch it yet.

to get 1/5 to have a denominator of 10, we need to multiply both the top and bottom of the fraction by 2 (because 2 x 5 is 10). we can do this because we're multiplying by 2/2, which is equal to 1. multiplying by 1 does not change the value of the fraction.

1 x 2 = 2, and 5 x 2 = 10, so our new fraction equivalent to 1/5 is 2/10.

now, we can add 3/10 + 2/10. when you add fractions, you add the numerators and keep the common denominators. so 3/10 + 2/10 = (3+2)/10 = 5/10. so 5/10 of the budget has been used.

to find out what fraction is left, we subtract 1 - 5/10. 1 is equal to any number over itself (as we saw earlier with 2/2) so we're subtracting 10/10 - 5/10. this gets us to 5/10. so 5/10 of the budget is left. 5/10 can be reduced to 1/2 in simplest form, since you can divide both 5 and 10 by their greatest common factor, which is 5. so 1/2 of the budget is left.